Bivariate moment simulation of coagulating and sintering nanoparticles in flames

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Abstract
The design/control of particle synthesis reactors is hampered by the cumbersome nature of simulation methods (such as “sectional” representations of the particle population balance equation) to track the evolution of coagulating, restructuring populations in complex flow environments. Bivariate PBE‐methods were investigated using generalizations of a recent Gaussian quadrature‐based “moment” approach (McGraw, 1997; Wright et al., 2001). A 9‐moment method was applied to an extensive data set recently obtained using a “seeded” laminar flame reactor with laser‐based, as well as TEM‐grid thermophoretic sampling. Alumina nano‐aggregate population evolution is predicted using available rate/transport laws (for coagulation, thermophoresis and sintering) and the efficacy is predicted, and, together with the efficacy of such simulation methods for parameter estimation, is also illustrated inferring a “best fit” activation energy for nanoparticle sintering. Variants/extensions of these techniques should enable their incorporation into, say, full PDF‐methods for turbulent synthesis reactors, using improved rate laws.